Vantage 1:
Allow (-1, 0, 1) to emerge from X = 0
These identities are co-emergent.
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
1 ≡ (X + 1) / X^2
0 ≡ (X + 1) / X^2 - 1
-1 ≡ (X + 1) / X^2 - 2
Allow a = φ
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
Allow (-1, 0, 1) and a = φ
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
Vantage 2:
Allow (-1, 0, 1) to emerge from X = 0
These identities are co-emergent. Allow (-♾️, 0, ♾️) in place of (-1,0,1)
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
1 ≡ (X + 1) / X^2
0 ≡ (X + 1) / X^2 - 1
-1 ≡ (X + 1) / X^2 - 2
Allow a = φ
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
Allow (-1, 0, 1) and a = φ
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
Vantage 3:
Allow (-1, 0, 1) to emerge from X = 0
These identities are co-emergent. Allow -♾️ = 0 = ♾️ in place of (-1,0,1)
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
1 ≡ (X + 1) / X^2
0 ≡ (X + 1) / X^2 - 1
-1 ≡ (X + 1) / X^2 - 2
Allow a = φ
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
Allow (-1, 0, 1) and a = φ
1 ≡ a + 1 ≡ X^2 + 1 ≡ X + 2 ≡ (1 / X) + 2
0 ≡ a ≡ X^2 ≡ X + 1 ≡ 1 + (1 / X)
-1 ≡ a - 1 ≡ X^2 - 1 ≡ X ≡ (1 / X)
